The First Boundary Value Problem in a Given Domain

Abstract

This chapter discusses the first boundary value problem for the Stokes system in bounded sectionaly-smooth domains and the Navier—Stokes system in domains with noncompact boundaries. Properties of differential operators in Holder, weighted Holder, and weighted Sobolev spaces are studied in Sections 4.1–4.3. In Section 4.4, we present a simple proof that the first boundary value problem for the Stokes system in a bounded three-dimensional domain, whose boundary consists of two smooth components intersecting under a non-zero varying angle, has a unique solution in weighted Sobolev spaces.